Results 51 to 60 of about 8,512 (209)

Modified Optimal Energy and Initial Memory of Fractional Continuous-Time Linear Systems

, 2010
Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables.
Mozyrska, Dorota, Torres, Delfim F. M.
core   +1 more source

Grüss type integral inequalities for generalized Riemann-Liouville k-fractional integrals [PDF]

Journal of Inequalities and Applications, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shahid Mubeen, Sana Iqbal
openaire   +2 more sources

Exponential Stability of Higher Order Fractional Neutral Stochastic Differential Equation Via Integral Contractors

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.
ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar, Dhanalakshmi Kasinathan, Ramkumar Kasinathan, Ravikumar Kasinathan   +3 more
wiley   +1 more source

Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions

Open Mathematics, 2021
In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by ...
Budak Huseyin, Kara Hasan, Ali Muhammad Aamir, Khan Sundas, Chu Yuming   +4 more
doaj   +1 more source

Fractional Euler-Lagrange differential equations via Caputo derivatives [PDF]

, 2011
We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler-Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given.
AA Kilbas, AB Malinowska, AB Malinowska, AB Malinowska, AB Malinowska, B Brunt van, D Baleanu, D Baleanu, D Baleanu, D Mozyrska, D Mozyrska, DFM Torres, F Riewe, GSF Frederico, GSF Frederico, GSF Frederico, I Podlubny, NRO Bastos, NRO Bastos, OP Agrawal, R Almeida, R Almeida, R Almeida, R Almeida, R Almeida, R Almeida, R Magin, RA El-Nabulsi, RA El-Nabulsi, TM Atanacković   +29 more
core   +3 more sources

Riemann-Liouville Generalized Fractional Integral Inequalities

WSEAS TRANSACTIONS ON MATHEMATICS
In this paper, we define Riemann-Liouville generalized fractional integral. Moreover, we obtained some significant inequalities for Riemann-Liouville generalized fractional integrals.
Sümeyye Ermeydan Çi̇ri̇ş, Hüseyi̇n Yildirim   +1 more
openaire   +1 more source

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals

Journal of Inequalities and Applications, 2017
Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established.
Praveen Agarwal, Mohamed Jleli, Muharrem Tomar   +2 more
doaj   +1 more source

Fractional Probability Theory of Arbitrary Order

Fractal and Fractional, 2023
A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability
Vasily E. Tarasov
doaj   +1 more source

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source